2. (3 points) (Repeated game) Consider the following two-player simultaneous move game.

Assume that 6 r

(i) The game is played thrice, i.e., repeated twice. For what values of r, can (x, x) in the rst two periods be obtained as the outcome of a subgame perfect Nash equilibrium of the repeated game? Explain your strategies and present the relevant calculations.

(ii) Suppose that the game is innitely repeated and each player has a discount factor . Find the minimum value of so that (x, x) in each period is the outcome of a subgame perfect Nash equilibrium of the (innitely) repeated game. Explain your strategies and present the relevant calculations.

In each part, consider what kinds of deviations one needs to examine. Then come up with the appropriate strategies and the relevant inequalities

T Player 2 w y 2 w 5,5 5,3 6,2 1,1 23,5 r. 7,10 2,7 y 2,6 10,7 8,8 2,11 z 1,1 7,2 11,2 3,3 Player 1 T Player 2 w y 2 w 5,5 5,3 6,2 1,1 23,5 r. 7,10 2,7 y 2,6 10,7 8,8 2,11 z 1,1 7,2 11,2 3,3 Player 1